SOLUTION: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited
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Question 126198: A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A home-based company produces both hand-knitted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation, where x is the number of scarves and y is the number of sweaters. Then graph the system of inequalities.
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x = no. of scarves; y = no. of sweaters:
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The labor (in hours) inequality:
2x + 14y =< 40
Arrange in the general (y=) form so we can graph it:
14y =< -2x + 40
y =< -(2/14)x + (40/14)
y =< -(1/7)x + 20/7
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Plot this equation:
For x = 0
y = -(1/7)(0) + 20/7
y = 20/7 or about 2.85
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For x = 7
y = -(1/7)(7) + (20/7)
y = -1 + 20/7
y = -(7/7) + (20/7)
y = +13/7 or about 1.85
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A table of the x/y coordinates:
x | y
-------
0 | 2.85
7 | 1.85
Join these two points with a straight-edge for the labor graph
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The production inequality:
x + y = 5
y = 5 - x
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Plot this equation:
For x = 0, then y = 5, obviously
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For x = 4
y = 5 - 4
y = 1
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The table for these x/y coordinates
x | y
-------
0 | 5
4 | 1
Join these to points for the production graph
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your graph should look like this:
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The area of feasibility would be at or below either line, whichever is lower
It's assumed that x and y => 0
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It looks like the best you could do is 3 scarfs and 2 sweaters
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